Set Theory |
Common terms and phrases
a₁ a₂ arbitrary assume Axiom of Choice B₁ bijective function called choice function cofinal cofinal subset continuum hypothesis contradiction Corollary define a function Definition Let denumerable set denumerable subset disjoint epsilon number equipotent equivalence relation example Exercise Set f₁ finite set function f graph greatest element hence Hint hypothesis of induction iel iel immediate successor inaccessible cardinal infinite cardinal number infinite sets initial segment intuitive isomorphism least element Let f Let G limit ordinal mathematics maximal element natural numbers nonempty nonlimit ordinal one-to-one correspondence order relation p-sequence paradoxes partially ordered class partially ordered set Proof properties Prove the following rational numbers reader real numbers recursion theorem satisfies subclass successor set sup{x Suppose surjective function Theorem Let transfinite transitive set unique upper bound wª¹a₁ well-ordered class well-ordered sets well-ordering theorem x₁ y₁